Some Questions on Material Objectivity Arising in Models of Porous Materials

Abstract

The paper is devoted to the analysis of nonobjective contributions to continuous models of porous materials. Explicit contributions appearing in momentum balance equations in noninertial reference systems influence Darcy’s law considered as a limit case of a multicomponent model, and render it nonobjective. On the other hand an implicit constitutive contribution of relative accelerations to partial momentum balance equations of multicom-ponent models violates the principle of material objectivity. These two types of contribution bear physically different significances. The former seems to be a natural consequence of body forces on relative motions of components. The latter is incompatible with principles of a macroscopical continuous model. Even if we ignore the principle of material objectivity, contributions of relative accelerations are either indistinguishable from other contributions or yield unacceptable modes of propagation of sound waves or both. Consequently, in contrast to the nonobjectivity of Darcy’s law, we conclude that such contributions should be ignored completely in the construction of macroscopical models of porous materials.